{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T12:42:57Z","timestamp":1782218577194,"version":"3.54.5"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He\u2019s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He\u2019s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.<\/jats:p>","DOI":"10.3390\/axioms10030191","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T10:54:35Z","timestamp":1629284075000},"page":"191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":83,"title":["Periodic Property and Instability of a Rotating Pendulum System"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1636-0559","authenticated-orcid":false,"given":"Ji-Huan","family":"He","sequence":"first","affiliation":[{"name":"School of Science, Xi\u2019an University of Architecture & Technology, Xi\u2019an 710055, China"},{"name":"School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China"},{"name":"National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou 215000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tarek S.","family":"Amer","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shimaa","family":"Elnaggar","sequence":"additional","affiliation":[{"name":"Kafrelsheikh Higher Institute of Engineering and Technology, Kafrelsheikh 33511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0413-5618","authenticated-orcid":false,"given":"Abdallah A.","family":"Galal","sequence":"additional","affiliation":[{"name":"Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta 31734, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"ref_1","first-page":"336","article-title":"Dynamics analysis of an impulsive stochastic model for spruce budworm growth","volume":"19","author":"Ji","year":"2021","journal-title":"Appl. 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